A p-adic analogue of a formula of Ramanujan

Dermot McCarthy, Robert Osburn

Research output: Contribution to journalArticle

37 Scopus citations

Abstract

During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures.

Original languageEnglish
Pages (from-to)492-504
Number of pages13
JournalArchiv der Mathematik
Volume91
Issue number6
DOIs
StatePublished - Dec 1 2008

    Fingerprint

Keywords

  • Gaussian hypergeometric series
  • Supercongruences

Cite this